TY - JOUR

T1 - C-Supplemented Subalgebras of Lie Algebras.

AU - Towers, David A.

PY - 2008

Y1 - 2008

N2 - A subalgebra $B$ of a Lie algebra $L$ is c-{\it supplemented} in $L$ if there is a subalgebra $C$ of $L$ with $L = B + C$ and $B \cap C \leq B_L$, where $B_L$ is the core of $B$ in $L$. This is analogous to the corresponding concept of a c-supplemented subgroup in a finite group. We say that $L$ is c-{\it supplemented} if every subalgebra of $L$ is c-supplemented in $L$. We give here a complete characterisation of c-supplemented Lie algebras over a general field.

AB - A subalgebra $B$ of a Lie algebra $L$ is c-{\it supplemented} in $L$ if there is a subalgebra $C$ of $L$ with $L = B + C$ and $B \cap C \leq B_L$, where $B_L$ is the core of $B$ in $L$. This is analogous to the corresponding concept of a c-supplemented subgroup in a finite group. We say that $L$ is c-{\it supplemented} if every subalgebra of $L$ is c-supplemented in $L$. We give here a complete characterisation of c-supplemented Lie algebras over a general field.

KW - Lie algebras

KW - c-supplemented subalgebras

KW - completely factorisable algebras

KW - Frattini ideal

KW - subalgebras of codimension one.

M3 - Journal article

VL - 18

SP - 717

EP - 724

JO - Journal of Lie Theory

JF - Journal of Lie Theory

IS - 3

ER -